Activist investor Carl Icahn has filed documents with the US Security and Exchange Commission today which reveal his purchase of an additional $1 billion worth of Apple stock. The move increases his holding to $3.6 billion and is a bolder move by Icahn to motivate the company’s board to increase its buyback program.

Yesterday, Icahn announced that he was going to purchase $500 million worth of Apple’s stock and then followed up the next day to repeat the process.

Calling it a “no brainer” of a move, Icahn believes his position is sound and issued a seven page letter to Apple shareholders to sell his case:

We believe, however, that this share repurchase authorization can and should be even larger, and effectuating that for the benefit of all of the company’s shareholders is the sole intention of our proposal. The company has recommended voting against our proposal for various reasons. It seems to us that the basis of its argument against our proposal is that the company believes, because of the “dynamic competitive landscape” and because its “rapid pace of innovation require[s] unprecedented investment, flexibility and access to resources”, it does not currently have enough excess liquidity to increase the size of its repurchase program.

Throughout Icahn’s letter, he makes reference to rumors that Apple will have larger screens for iPhone and iPads, along with speculation about what company CEO Tim Cook’s new “product category” will be. The lengthy correspondence also says an Apple TV would represent one opportunity for the company to take, along with other hardware advances, although he doesn’t go into great specifics.

And here’s the kicker in the whole thing: Icahn wants Apple to implement his rather extreme buyback proposal, which is way more than anything that the company ever announced. He says that based on the company’s current circumstances, the $50 billion amount is appropriate. Here’s his rationale (emphasis TNW’s):

The Board may argue that much of its cash and earnings are international and therefore subject to a repatriation tax if returned to the United States to repurchase shares. While this is true, we question why the company would not simply borrow the money in the Unites States to the extent it deems its domestic cash of $36 billion and domestic earnings are insufficient. Given that the company has $130 billion of net cash and $40 billion of expected annual earnings, and the fact that it is hard to find a better time in history to borrow money, a $50 billion share repurchase over the course of fiscal year 2014 seems more than reasonable to us. Today, Apple’s outstanding ten year bonds yield 3.63%, and its five year bonds yield 2%. Apple could either continue to carry this debt, repay it from its domestic earnings over time, or repatriate cash from abroad upon the passage of corporate tax reform.

Apple announced its buyback program in 2012 and it has gradually increased from $10 billion to $60 billion in 2013. Around this time, Icahn entered the picture first saying with a tweet that he had a “large position” in the company and voiced his opinion that it was undervalued. In December, Apple urged its shareholders to vote against Icahn’s $50 billion proposal and it’s still on the company’s annual shareholder meeting which is scheduled for February 28.

It’s worth noting that Icahn’s stake still prevents him from being one of the largest shareholders, but the fact that he holds this much stock could give him more leverage to pursue his cause.

Shares in Apple are up 0.77 percent today to $555.77 following Icahn’s announcement.

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